Stochastic Yield Research Articles

Coordination for contract farming supply chain with stochastic yield and demand under CVaR criterion

This paper analyzes the optimal production and pricing decisions in an agricultural supply chain formed by contract farming scheme consisting of an agribusiness firm and multiple risk-averse farmers. The effects of yield and demand uncertainties and the farmer’s risk aversion on the optimal decisions of the production quantity, wholesale price and retail price are analyzed. Our analyses provide managerial insights on the contract terms of the agricultural supply chain. We show that the production quantity decreases as the farmer is more risk-averse and faces higher yield uncertainty, while the retail price subsequently increases. However, the wholesale price is influenced by the interaction effect of the farmer’s risk aversion and yield uncertainty. The retail price is influenced by the interaction effect of demand uncertainty and price elasticity. In particular, we show that the loss due to the decentralized decisions increases as the farmer is more risk-averse and yield uncertainty is higher. Thus, a RPG (Revenue sharing + Production cost sharing + Guaranteed money) mechanism is developed to facilitate the coordination of the agricultural supply chain under uncertainty environment with risk-averse agents based on contract farming practices. The cost allocation ratio of the RPG mechanism borne by the agribusiness firm increases in the yield and market demand uncertainties and decreases in the farmer’s risk aversion. Specially, if the farmer is extremely risk averse, as well as the yield and demand becomes extremely higher, the RPG mechanism cannot achieve perfect coordination of the agricultural supply chain.

Optimal order split between local and global suppliers under stochastic yield and demand

Optimal order split between local and global suppliers under stochastic yield and demand

Optimal order split between local and global suppliers under stochastic yield and demand

Consider a firm facing an infinite horizon inventory problem with two suppliers, a local one with zero lead time and a global one with positive lead time. Assume that both suppliers have variable yields with known mean and standard deviation of yields, but no assumption made about the distribution of yield. Order cycle length is assumed to be a given industry standard supply window of unit length. Depending on the lead time taken t by the global supplier, the unit period is divided into two segments, 0 to t and t to 1. Demand is independent and uniform with different parameters for each of the two segments. The firm also has different holding and shortage costs in each segment and has the same selling price per unit for the entire period. We solve the problem of finding the optimal order quantities for each supplier that maximises the expected discounted profit for the entire horizon. We also solve an extension of this problem, where the length of the period along with order quantities are decision variables by proposing a robust heuristic procedure.

High-throughput stochastic tensile performance of additively manufactured stainless steel

An adage within the Additive Manufacturing (AM) community is that “complexity is free”. Complicated geometric features that normally drive manufacturing cost and limit design options are not typically problematic in AM. While geometric complexity is usually viewed from the perspective of part design, this advantage of AM also opens up new options in rapid, efficient material property evaluation and qualification. In the current work, an array of 100 miniature tensile bars are produced and tested for a comparable cost and in comparable time to a few conventional tensile bars. With this technique, it is possible to evaluate the stochastic nature of mechanical behavior. The current study focuses on stochastic yield strength, ultimate strength, and ductility as measured by strain at failure (elongation). However, this method can be used to capture the statistical nature of many mechanical properties including the full stress-strain constitutive response, elastic modulus, work hardening, and fracture toughness. Moreover, the technique could extend to strain-rate and temperature dependent behavior. As a proof of concept, the technique is demonstrated on a precipitation hardened stainless steel alloy, commonly known as 17-4PH, produced by two commercial AM vendors using a laser powder bed fusion process, also commonly known as selective laser melting. Using two different commercial powder bed platforms, the vendors produced material that exhibited slightly lower strength and markedly lower ductility compared to wrought sheet. Moreover, the properties were much less repeatable in the AM materials as analyzed in the context of a Weibull distribution, and the properties did not consistently meet minimum allowable requirements for the alloy as established by AMS. The diminished, stochastic properties were examined in the context of major contributing factors such as surface roughness and internal lack-of-fusion porosity. This high-throughput capability is expected to be useful for follow-on extensive parametric studies of factors that affect the statistical reliability of AM components.

A stochastic recurrence equations approach for score driven correlation models

ABSTRACTWe describe stationarity and ergodicity (SE) regions for a recently proposed class of score driven dynamic correlation models. These models have important applications in empirical work. The regions are derived from sufficiency conditions in Bougerol (1993) and take a nonstandard form. We show that the nonstandard shape of the sufficiency regions cannot be avoided by reparameterizing the model or by rescaling the score steps in the transition equation for the correlation parameter. This makes the result markedly different from the volatility case. Observationally equivalent decompositions of the stochastic recurrence equation yield regions with different shapes and sizes. We use these results to establish the consistency and asymptotic normality of the maximum likelihood estimator. We illustrate our results with an analysis of time-varying correlations between U.K. and Greek equity indices. We find that also in empirical applications different decompositions can give rise to different conclusions regarding the stability of the estimated model.

Risk shaping in production planning problem with pricing under random yield

In this paper, we address a basic production planning problem with price dependent demand and stochastic yield of production. We use price and target quantity as decision variables to control the risk of low production yield. The value of risk control becomes more important especially for products with short life cycle where high losses are unbearable in the short run. In this cases, optimization of a solely scalar function of profit is not sufficient to control the risk. We apply Conditional Value at Risk (CVaR) measure to model the risk preferences of the producer. The producer is interested in shaping the risk by bounding from below the means of α-tail distributions of profit for different values of α. The resulting model is nonconvex. We propose an efficient solution algorithm and present a sufficient optimality condition.

Coordinating a vendor–buyer supply chain with stochastic demand and uncertain yield

The paper develops a single-vendor single-buyer supply chain model with stochastic demand and uncertain yield where the vendor delivers the buyer’s order quantity in a number of shipments. We formulate the model considering instantaneous/non-instantaneous supplies from the vendor to the buyer and that the buyer’s replenishment time interval does/doesn’t depend upon the input. The optimal shipment policy is determined by maximizing the average expected profit of the whole supply chain. The model is further extended to consider a revenue sharing contract to align incentives of decentralized partners within the supply chain. Numerical examples are provided to illustrate the developed models. It is observed from the numerical study that the coordinated (integrated) policy is beneficial in comparison to the individual policies made by the supply chain partners.

Implementation of Stochastic Yield Curve Duration and Portfolio Immunization Strategies

In this paper, we propose an implementation method for a new concept of stochastic duration which can be used to measure the sensitivity of complex bond portfolios with respect to the fluctuations of the yield surface. Our approach relies on a first order approximation of a chaos expansion in the direction of the yield surface, whose dynamics is described by the Musiela equation. Using the latter technique, we obtain an infinite-dimensional generalization of the classical Macaulay duration, which can be interpreted as the derivative of a first order approximation of a Taylor series on locally convex spaces.

An Analytically Tractable Model for Pricing Multiasset Options with Correlated Jump-Diffusion Equity Processes and a Two-Factor Stochastic Yield Curve

This paper shows how to value multiasset options analytically in a modeling framework that combines both continuous and discontinuous variations in the underlying equity or foreign exchange processes and a stochastic, two-factor yield curve. All correlations are taken into account, between the factors driving the yield curve, between fixed income and equity as asset classes, and between the individual equity assets themselves. The valuation method is applied to three of the most popular two-asset options.

Estimating The Maximum Value of Crop Hail Insurance Under Stochastic Yield and Price Risk

ABSTRACTThe objective of this article is to estimate the maximum value of crop hail insurance according to the financial extent of hail risk's impact on the enterprise in two regions, North West (low hail risk area) and Mpumalanga (high hail risk area). The difference in the cumulative probability distributions of the Net Present Value (NPV) of the margin after interest and tax in the event of hail and in the event of no hail will provide a graphic indication of the financial impact of hail. To determine if the decision maker is willing to pay in order to remove the impact of hail on the enterprise, the utility weighted risk premium (UWRP) must be calculated with the use of stochastic efficiency with respect to a function (SERF) analysis. The calculated maximum benefit (or UWRP) that the decision maker will receive through the elimination of hail will set the upper limit for the cost of crop hail insurance. The results indicate that hail does have a negative impact on the financial position of the farms in North West and Mpumalanga. The effect of hail risk in Mpumalanga is, however, more severe. The calculated maximum benefit (UWRP) from the elimination of hail damage in two regions is R83.50/hectare in North West and R708.70/hectare in Mpumalanga. The conclusion can thus be made that decision makers in both regions will be willing to pay for crop hail insurance, but much more so in Mpumalanga than in North West.

Strategy of Production and Ordering in Closed-loop Supply Chain under Stochastic Yields and Stochastic Demands

A closed-loop supply chain system consisting of one manufacturer with random yield and one retailer with random demand is discussed in this paper. The models of expected profit of supply chain system are founded under centralized decision and decentralized decision, respectively. The optimal strategies of yield and order are obtained in two modes. It is proved that the order of retailer is not affected by yield randomness. That is showed by numerical example, the results show: the scheduled production of new product for manufacture will decrease and the total profit and each participant of supply chain will increase as recovery price increases, when the cost of remanufacturing production is lower than the new product.

A stochastic crystal plasticity framework for deformation of micro-scale polycrystalline materials

In this paper we investigate the stochastic behavior in the mechanical response of polycrystalline materials consisting of few grains to hundreds of grains at micron size scales. We study the transition from stochastic (at small scale) to deterministic (at large scale) deformation behavior in polycrystalline samples using both simulation and nanoindentation experiments. Specifically, we develop a stochastic crystal plasticity model combining a Monte Carlo method with a polycrystal continuum dislocation dynamics model in a self-consistent viscoplasticity framework. Using this framework, we numerically calculate the mechanical properties of the polycrystal and gather randomized sampling data of the flow stress. The numerical results are compared to nanoindentation experimental data from three samples with ultra-fine grain structures manufactured via the severe plastic deformation method. The controlling mechanisms of the observed stochastic yield behavior of polycrystals are then discussed using simulations and experimental results. Our results suggest that it is the combination of stochastic plasticity at small scales (where the strength may vary from grain to grain) coupled with the effects of microstructural features such as grain size distribution and crystallite orientations that govern the uncertainty in the mechanical response of the polycrystalline materials. The extent of the uncertainty is correlated to the “effective cell size” in the sampling procedure of the simulations and experiments. The simulations and experimental results demonstrate similar quantitative behavior in terms of coefficient of variation within the same effective cell size.

Production planning problem with pricing under random yield: CVaR criterion

In this paper, we address a basic production planning problem with price dependent demand and stochastic yield of production. We use price and target quantity as decision variables to lower the risk of low yield. The value of risk control becomes more important especially for products with short life cycle. This is because, the profit implications of low yield might be unbearable in the short run. We apply Conditional Value at Risk (CVaR) to model the risk. CVaR measure is a coherent risk measure and thereby having nice conceptual and mathematical underpinnings. It is also widely used in practice. We consider the problem under general demand function and general distribution function of yield and find sufficient conditions under which the problem has a unique local maximum. We also both analytically and numerically analyze the impact of parameter change on the optimal solution. Among our results, we analytically show that with increasing risk aversion, the optimal price increases. This relation is opposite to that of in Newsvendor problem where the uncertainty lies in demand side.

On the Performance of the Comonotonicity Approach for Pricing Asian Option in Some Benchmark Models from Equities and Commodities

In this paper we investigate the applicability of the Albrecher et. al. (2005) comonotonicity approach in the context of various benchmark models for equities and commodities. Instead of classical Levy models as in Albrecher et. al. we focus on the Heston stochastic volatility model, the constant elasticity of variance (CEV) model and Schwartz' 1997 stochastic convenience yield model. We show that the method delivers rather tight upper bounds for the prices of Asian Options in these models and as a by product delivers super-hedging strategies which can be easily implemented.

Can Spanned Term Structure Factors Drive Stochastic Yield Volatility?

The ability of the usual factors from empirical arbitrage-free representations of the term structure -- that is, spanned factors -- to account for interest rate volatility dynamics has been much debated. We examine this issue with a comprehensive set of new arbitrage-free term structure specifications that allow for spanned stochastic volatility to be linked to one or more of the yield curve factors. Using U.S. Treasury yields, we find that much realized stochastic volatility cannot be associated with spanned term structure factors. However, a simulation study reveals that the usual realized volatility metric is misleading when yields contain plausible measurement noise. We argue that other metrics should be used to validate stochastic volatility models

Hedging of long term zero-coupon bonds in a market model with reinvestment risk

We present a computational methodology to value and hedge long term zero-coupon bonds trading in short and medium term ones. For this purpose we develop a discrete time stochastic yield curve model with limited availability of maturity dates at a fixed time point and newly issued bonds at future time points. This involves reinvestment risk and there is no perfect hedging strategy available for long term liabilities. We calibrate the model to market data and describe optimal hedging strategies under a given risk tolerance. These considerations provide a natural extrapolation of the yield curve beyond the last liquid maturity date, and a framework which allows to value long term insurance liabilities, for instance, under Solvency 2. Moreover, we determine the optimal trading strategy replicating the liabilities under the given risk tolerance.

Stochastic Corn Yield Response Functions to Nitrogen for Corn after Corn, Corn after Cotton, and Corn after Soybeans

Deterministic and stochastic yield response plateau functions were estimated to determine the expected profit-maximizing nitrogen rates, yields, and net returns for corn grown after corn, cotton, and soybeans. The stochastic response functions were more appropriate than their deterministic counterparts, and the linear response stochastic plateau described the data the best. The profit-maximizing nitrogen rates were similar for corn after corn, cotton, and soybeans, but relative to corn after corn, the expected corn yield plateaus increased by 12% and 16% after cotton and soybeans, respectively. Expected net returns increased for corn after cotton and soybeans relative to corn after corn.

Stationarity and Ergodicity Regions for Score Driven Dynamic Correlation Model

We describe stationarity and ergodicity (SE) regions for a recently proposed class of score driven dynamic correlation models. These models have important applications in empirical work. The regions are derived from sufficiency conditions in Bougerol (1993) and take a non-standard form. We show that the non-standard shape of the sufficiency regions cannot be avoided by reparameterizing the model or by rescaling the score steps in the transition equation for the correlation parameter. This makes the result markedly different from the volatility case. Observationally equivalent decompositions of the stochastic recurrence equation yield regions with different sizes and shapes. We illustrate our results with an analysis of time-varying correlations between UK and Greek equity indices. We find that also in empirical applications different decompositions can give rise to different conclusions regarding the stability of the estimated model.

A New Class of Local Correlation Models

Allowing correlation to be local, i.e., state-dependent, in multi-asset models allows better hedging by incorporating correlation moves in the delta. When options on a basket, be it a stock index, a cross FX rate, or an interest rate spread, are liquidly traded, one may calibrate a local correlation to these option prices. In this article we introduce a new family of local correlation models from which one can pick a model that not only calibrates to the basket smile but also has extra desirable properties, like fitting a view on correlation skew, mimicking historical correlation, or matching prices of exotic options. The family is built using the particle method and the procedure is easily adapted to calibrate path-dependent volatility models, path-dependent correlation models, and to include stochastic rates, stochastic dividend yield, and stochastic volatility.

Coordination of Agricultural Products Supply Chain with Stochastic Yield by Price Compensation

In this paper, coordination problem of agricultural products supply chain with stochastic yield is studied based on prices compensation strategy. The agricultural producing is influenced by the natural conditions, and the yield is uncertain. While agricultural products is rigid demand goods, the fluctuations of yield cause greater volatility of prices. The two- echelon supply chain with one supplier and one retailor is studied, and the mathematical model is constructed. The model showed that prices compensation strategy is Pareto improvement for agricultural products supply chain with stochastic yield, and it also incentive agricultural products supplier to rise the production plan and balance the profit allocation of supply chain.